This is one of a series of units intended for both preservice and inservice elementary school teachers to satisfy a need for materials on "new mathematics" programs which (1) are readable on a self basis or with minimal instruction, (2) show the pedagogical objectives and uses of such mathematical structural ideas as the field axioms, sets, and logic, and (3) relate mathematics to the "real world," its applications, and other areas of the curriculum. In this unit, the grouping model for applying multiplication and division is explored and extended through various sub-models as an illustration of the conceptual model approach to the applications of mathematics. The four parts of this unit are (1) multiplication, (2) whole number division without a remainder, (3) the quantity models for fractions and multiplication, and (4) a quantity model for division of fractions. (RP)